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The Journal of Neuroscience, November 15, 2002, 22(22):10053-10065
A Synaptic Explanation of Suppression in Visual Cortex
Matteo Carandini1, David J Heeger2, and Walter Senn3 1 Institute of Neuroinformatics, University of Zurich and Swiss Federal Institute of Technology, CH-8057 Zurich, Switzerland, 2 Department of Psychology, Stanford University, Stanford, California 94305, and 3 Institute of Physiology, University of Bern, CH-3012 Bern, Switzerland
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
The responses of neurons in the primary visual cortex (V1) are suppressed by mask stimuli that do not elicit responses if presented alone. This suppression is widely believed to be mediated by intracortical inhibition. As an alternative, we propose that it can be explained by thalamocortical synaptic depression. This explanation correctly predicts that suppression is monocular, immune to cortical adaptation, and occurs for mask stimuli that elicit responses in the thalamus but not in the cortex. Depression also explains other phenomena previously ascribed to intracortical inhibition. It explains why responses saturate at high stimulus contrast, whereas selectivity for orientation and spatial frequency is invariant with contrast. It explains why transient responses to flashed stimuli are nonlinear, whereas spatial summation is primarily linear. These results suggest that the very first synapses into the cortex, and not the cortical network, may account for important response properties of V1 neurons.
Key words: suppression; masking; depression; inhibition; cortex; thalamus; orientation; contrast
INTRODUCTION
Neurons in the primary visual cortex (V1) rapidly adjust their gain, or responsiveness, to changes in visual stimulus contrast (for review, see Carandini et al., 1997
). This gain control is weaker in the lateral geniculate nucleus (LGN) and is the object of a number of computational models (Albrecht and Geisler, 1991
The first phenomenon is contrast saturation. Although responses of lateral geniculate neurons increase with stimulus contrast over the full range of contrasts, at high contrast, responses of V1 neurons reach a plateau (Albrecht and Hamilton, 1982
The second phenomenon is cross-orientation suppression. Responses to a test with optimal orientation are partially suppressed by superposition of a mask with orthogonal orientation (Bishop et al., 1973
Suppression is generally interpreted as evidence for intracortical inhibition (Blakemore and Tobin, 1972
However, recent results cast doubt on these views and suggest that suppression cannot come from cortical cells. First, cross-orientation inhibition is supported by some studies (Morrone et al., 1987
We propose an alternative, feedforward mechanism for gain control in the visual cortex, where the relevant signals originate in the LGN. In particular, we suggest that gain control operates through synaptic depression at thalamocortical synapses. Depression at these synapses has been observed in vitro (Stratford et al., 1996
Portions of this work appeared in a conference abstract (Carandini et al., 2001
MATERIALS AND METHODS
We considered a basic model of V1 simple cell summing appropriate LGN inputs, and we endowed thalamocortical synapses with a depression mechanism. To concentrate on the effects of synaptic depression, we kept our model extremely simple and did not include detailed aspects of neuronal biophysics (Koch, 1999
Here we briefly describe the model, details of which are given in the Appendix.
Receptive fields. Our model V1 simple cell is based on the original proposal by Hubel and Wiesel (1962)
This pattern of excitation is complemented by subtractive inhibition arranged in "push-pull" manner, whereby excitation by ON-center neurons is matched by inhibition by OFF-center neurons and vice versa (Palmer and Davis, 1981
With the exception of a threshold for spike generation, we model LGN neurons as responding linearly (Enroth-Cugell and Robson, 1966
Synaptic depression. In addition to this classic arrangement of synaptic inputs, we postulate that thalamocortical connections exhibit synaptic depression. Depression can be described by the following equation (Senn et al., 2001
where p is the probability of synaptic transmission, f is the presynaptic firing rate, and u is a utilization parameter. This expression is simplified from a more detailed model involving the arrival times of individual presynaptic spikes (Abbott et al., 1997
(1) R. If the depression term were absent, p would be constant, and the synapse would operate linearly. Incidentally, the expression above is identical to one describing photopigment depletion in the retina (Rushton and Henry, 1968
In our simulations, the utilization parameter was u = 0.75, at the high end of the range (0.1-0.95) found in vitro (Tsodyks and Markram, 1997
RESULTS
We start by describing the effects of depression in a single synapse and then go on to illustrate a variety of properties of our model V1 neuron.
Suppression in a single synapse
Synaptic depression causes the response to a presynaptic step of current to be transient (Fig. 1A). As presynaptic firing rate steps up (Fig. 1A, second row), postsynaptic current increases rapidly but is cut short by synaptic depression, resulting in a sharp transient followed by a plateau and then by recovery at the end of the step (Fig. 1A, third row). Although attenuated by the filtering properties of the membrane, this transient is still present in the membrane potential responses (Fig. 1A, bottom).
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Figure 1. Input-output properties of a depressing synapse. A-E, Effects of injection of various waveforms into the presynaptic (Presyn) neuron. Top row, Injected current Ipre (A, step; B-D, 2 Hz sinusoids with amplitudes 0.025, 0.1, and 0.4; E, sinusoid with amplitude 0.1 plus white noise with amplitude 0.25). Second row, The resulting presynaptic firing rate f. Third row, The output of the depressing synapse; postsynaptic (Postsyn) current Ipost = p u f. Bottom row, Postsynaptic potential V, which is Ipost after filtering by the passive properties of the neuron. To avoid unnecessary free parameters, we have used the same units, spikes per second, for currents, potentials, and firing rates. F, The 2 Hz component of presynaptic firing rate f (right axis, dashed lines) and of postsynaptic current Ipost (left axis, symbols) as a function of the amplitude of presynaptic sinusoidal current Ipre.
Synaptic depression is much more rapid than the subsequent recovery. As explained in the Appendix, the effective time constant
A depressing synapse exhibits saturation. Consider first the presynaptic firing rate responses to sinusoidal injected currents (Fig. 1B-D, second row). Because the presynaptic neuron has a resting firing rate of 10 spikes/sec, small current injections result in a sinusoidal firing rate, but larger ones are clipped where firing rates would be negative. The relationship between presynaptic current and firing rate is nonetheless primarily linear (Fig. 1F, right axis). The effects of synaptic depression can be observed in the postsynaptic current (Fig. 1B-D, third row). Depression distorts the postsynaptic current, which is not sinusoidal but exhibits transient increases followed by more tonic responses. Distortion increases with presynaptic firing rate, causing a substantial saturation in response amplitude (Fig. 1F, left axis). This saturation is a well known property of synaptic depression (Abbott et al., 1997
In addition to saturation, a depressing synapse exhibits divisive suppression. Adding noise to the injected current (Fig. 1E) increases synaptic depression. This effect is best appreciated in the membrane potential response (Fig. 1, bottom), where high-frequency components of the postsynaptic current have been filtered out by the passive properties of the membrane. The noise current partially suppresses the responses to the sinusoidal current (compare Fig. 1C,E, bottom). This suppression is divisive (Fig. 1F, rightward shift of curves on a logarithmic scale), as if the noise had divided the amplitudes of the injected sinusoidal test currents by a fixed scale factor.
Thanks to saturation and suppression exhibited by depressing synapses, our model simple cell displays many properties of real simple cells.
Contrast saturation
Our model simple cell exhibits contrast saturation; responses to an optimally oriented drifting grating level off at high stimulus contrasts (Figs. 2, 3). The firing rate of an ON-center LGN cell increases when the bright bars of the grating pass over its receptive field (and likewise for dark bars for an OFF-center LGN cell). When the firing rate of an LGN cell increases, probability of transmission at its synapses decreases. The pattern of synaptic depression across the spatial array of LGN receptive fields is itself a grating, which closely trails the leftward moving stimulus (Fig. 2A, second row) (Senn et al., 2001
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Figure 2. Responses to gratings and plaids. A, Vertical grating at 25% contrast drifting to the left at 4 Hz. Top row, Two stimulus frames, at t = 125 and 250 msec. Second row, Corresponding spatial maps of synaptic depression, with intensity proportional to probability of transmission for synapses from LGN ON-center neurons. Third row, Postsynaptic currents in the V1 neuron, from ON-center LGN neurons, for the first two stimulus cycles. Fourth row, Same for OFF-center LGN inputs. Bottom row, Average firing rate responses to two stimulus cycles. B, Same grating as in A, at 50% contrast. Saturation is evident; firing rates are less than twice those in A. C, Same grating as in A but oriented horizontal and drifting upward. D, Plaid obtained by summing the gratings from A and C. Suppression is visible because firing rates are less than those in A.
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Figure 3. Dependence of response on grating contrast and orientation. A, Response versus stimulus contrast for three stimulus orientations. Curves fitted to data are hyperbolic ratios (Albrecht and Hamilton, 1982
When stimulus contrast is increased by a factor of two (Fig. 2B), firing rates of LGN neurons also increase by a factor of two, causing the probability of synaptic transmission to drop (compare Fig. 2A,B, second row). The increase in synaptic depression causes a greater reduction in individual synaptic currents, so that synaptic currents increase only slightly (compare Fig. 2A,B, third and fourth rows). The firing rate response of the neuron barely increases at all (Fig. 2A,B, bottom). Without depression, currents in Figure 2B would be twice as large as those in Figure 2A. Instead, as contrast increases, responses saturate and reach a plateau (Fig. 3A).
Our model correctly predicts that responses plateau at a given contrast level regardless of firing rate and regardless of stimulus orientation and spatial frequency (Albrecht and Hamilton, 1982
As a consequence, our model correctly predicts that even in the face of contrast saturation, the selectivity of a neuron for stimulus attributes such as orientation or spatial frequency is invariant with stimulus contrast (Albrecht and Hamilton, 1982
Cross-orientation suppression
Our model predicts suppression because two superimposed stimuli cause more synaptic depression than either stimulus alone. This behavior is illustrated by simulating responses to a plaid, the sum of an optimally oriented test grating, and an orthogonal mask grating (Fig. 2D). Responses to this plaid are clearly smaller than to test alone, although the mask did not elicit any response on its own. The reason for this suppression can be observed in the maps of stimulus and of probability of synaptic transmission (Fig. 2). As the plaid moves up and to the left, those parts of it that excite ON-center cells (Fig. 2D, top, white blobs) encounter regions that have stronger depression (Fig. 2D, second row, dark blobs) than in the case of individual gratings (Fig. 2A, second row). A similar argument could be made for the probability of transmission for synapses from OFF-center cells (data not shown). Therefore, as the vertical component of the plaid moves laterally, it encounters regions where the probability of transmission has been lowered by the passage of the horizontal component. Without depression, the firing rate in Figure 2D would be close to that in Figure 2A.
Because the effects of synaptic depression are divisive, the model correctly predicts that the effects of suppression are divisive (Bonds, 1989
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Figure 4. Cross-orientation suppression. Responses for plaids composed of an optimally oriented test grating and an orthogonal mask grating (as in Fig. 2D). Gray levels correspond to different mask contrasts. Curves are hyperbolic ratios (Albrecht and Hamilton, 1982
Moreover, the model easily explains the spatial extent of cross-orientation suppression. Orthogonal gratings cause suppression only when they are presented in a region well within the receptive field (DeAngelis et al., 1992
Time course of suppression
Our model correctly predicts that cross-orientation suppression is very fast. In fact, suppression from within the receptive field appears to have the same latency as the responses themselves, indicating that its mechanism requires less than a few milliseconds (Smith et al., 2001
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Figure 5. Time course of cross-orientation suppression; simulation of an experiment similar to that of Smith et al. (2001)
Orientation tuning of suppression
Up to now, we have only considered suppression from orthogonal masks. When measured with drifting gratings, however, suppression can be obtained with masks of any orientation (Morrone et al., 1982
) are smaller than when the mask is absent (Fig. 6A, straight dashed line). Without depression, the two would be identical. In this simulation of an experiment by Bonds (1989)
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Figure 6. Orientation dependence of suppression by drifting and flashed masks. Responses to an optimally oriented test as a function of mask orientation. For comparison, the curved dashed line shows responses to tests of different orientations, in the absence of a mask. The straight dashed line is the response to optimal orientation. A, Suppression by superimposed drifting gratings. This is a simulation of an experiment by Bonds (1989)
The results of the above experiment are different if instead of drifting gratings, one uses briefly flashed bars. If the interval between the two is short (tens to hundreds of milliseconds), the response to a test flashed bar is substantially reduced by a previous presentation of a mask flashed bar (Nelson, 1991a
In summary, our model explains a discrepancy in the literature regarding the orientation selectivity of suppression. Suppression has been reported to be present with a broad range of mask orientations, often equally strong when mask and test are parallel as when they are orthogonal (Morrone et al., 1982
Suppression with fast stimuli
Because our model explains suppression without recourse to intracortical inhibition, it correctly predicts that stimuli do not have to elicit spikes in V1 to cause suppression. An example of this behavior has been observed with stimuli drifting very fast. The temporal frequency tuning of suppression is broad (Morrone et al., 1982
These results would be hard to explain with intracortical mechanisms but are easily explained by our model (Fig. 7). We have designed our model LGN neurons to respond maximally to gratings drifting at ~10 Hz and still give a good response to gratings drifting twice as fast (Fig. 7A). In contrast, we have designed our model V1 neuron to respond maximally to gratings drifting at ~2 Hz and to give barely any response to gratings drifting at 20 Hz (Fig. 7B). Although our V1 neuron does not respond to them, mask gratings drifting as fast as 25 Hz give strong suppression (Fig. 7C). Indeed, because suppression is driven by LGN responses, the dependence of suppression on mask drift rate (Fig. 7C) is very similar to that of LGN responses (Fig. 7A). As illustrated by Freeman et al. (2002)
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Figure 7. Suppression by masks drifting at different rates. This is a simulation of an experiment by Freeman et al. (2002)
Moreover, our model explains why suppression is immune to visual adaptation effects that follow prolonged stimulation (Freeman et al., 2002
Suppression with white noise
Dynamic white noise stimuli (which look like "snow" in an untuned television) give powerful suppression, although they do not elicit much of a response in V1 neurons (Morrone et al., 1982
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Figure 8. Suppression with dynamic noise (same format as Fig. 2). A, White noise stimulus. B, Grating with 10% contrast, drifting at 4 Hz with optimal orientation and spatial frequency for the model V1 neuron. C, Superposition of white noise and drifting grating. Although it elicits minimal responses in the V1 neuron, the white noise stimulus is a powerful mask.
A similar argument can be made for gratings of low spatial frequency. Although cat V1 neurons are typically bandpass in spatial frequency, the spatial frequency tuning of suppression is often low-pass, similar to that of LGN neurons (Morrone et al., 1982
Suppression with contrast-reversing stimuli
In an elegant experiment to probe the source of suppression, Morrone et al. (1982)
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Figure 9. Suppression from a contrast-reversing mask grating (same format as Fig. 2), simulating the experiment of Morrone et al. (1982)
Linear properties
The effects that we have described are major failures of linearity. Contrast saturation is a nonlinearity because doubling stimulus contrast does not double response amplitude. Suppression is a nonlinearity because response to the sum of test and mask is not equal to the sum of responses to those stimuli when presented alone. Synaptic depression explains these phenomena because it is a nonlinear mechanism.
Nonetheless, V1 simple cells also exhibit behaviors that appear linear (for review, see De Valois and De Valois, 1988
First, simple cell responses to sinusoidal temporal modulation are approximately sinusoidal, as would be predicted by a linear model (Maffei and Fiorentini, 1973
Second, selectivity of simple cells for spatial stimulus attributes such as orientation or spatial frequency can be derived from the shape of the receptive field, as would be predicted by a linear model (Hubel and Wiesel, 1962
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Figure 10. Linearity of spatial summation; simulation of the experiment by Movshon et al. (1978a)
Recent studies have pointed out that synaptic depression might also explain a large class of nonlinearities of temporal summation (Chance et al., 1998
To summarize, our proposed mechanism to control neuronal responsiveness, thalamocortical synaptic depression, spares the linearity of spatial summation of the neuron. Spatial averaging of temporally nonlinear inputs allows our model neuron to exhibit some well known linear properties of simple cells.
DISCUSSION
We have proposed a biophysical foundation for the control of cortical responsiveness, thalamocortical synaptic depression, which is alternative to the common view based on intracortical inhibition. The model that we propose successfully explains saturation, suppression, and other phenomena ascribed previously to intracortical inhibition.
Our model can also account for properties that would be hard to explain with intracortical inhibition. First, the model explains how suppression can operate within a few milliseconds (Fig. 5); the intracortical inhibition model would predict longer latencies. Second, our model explains how suppression from drifting gratings is equally strong for all orientations, whereas suppression from flashed bars is strong only at the preferred orientation (Fig. 6); the intracortical inhibition model would predict equal orientation tuning for both types of suppression. Third, our model explains why stimuli that elicit good responses in the LGN but poor responses in the V1, such as gratings with fast drift rates (Fig. 7) and white noise (Fig. 8), can give rise to powerful suppression; the intracortical inhibition model would predict weak suppression. Fourth, our model explains why suppression is immune to visual adaptation effects that follow prolonged stimulation (Freeman et al., 2002
Nonetheless, there is a result that is predicted by intracortical inhibition but not by thalamocortical synaptic depression; it has been reported that blocking GABAA receptors removes cross-orientation suppression (Morrone et al., 1987
Mechanisms controlling cortical responsiveness
In addition to cross-orientation suppression, there are two classes of phenomena considered to be primarily cortical and to control the responsiveness of V1 neurons: surround suppression and visual adaptation. Both are likely to be explained by mechanisms different from synaptic depression.
Surround suppression is the phenomenon whereby mask stimuli located somewhat outside the classical receptive field of a neuron can reduce responses of V1 neurons to test stimuli located in the receptive field (for review, see Fitzpatrick, 2000
Visual adaptation is the phenomenon whereby prolonged stimulation of a V1 neuron reduces the subsequent responses of a neuron (Maffei et al., 1973
10-15 mV (Carandini and Ferster, 1997
We can then begin to assign different physiological mechanisms to different phenomena affecting responsiveness in the primary visual cortex. There are three main physiological mechanisms: (1) synaptic depression, (2) intracortical inhibition, and (3) intrinsic cellular mechanisms. We propose that each of these mechanisms is principally responsible for one type of gain control phenomenon:
1. Synaptic depression is principally responsible for cross-orientation suppression. This type of suppression is fast (a few milliseconds), monocular, present only within the receptive field, obtained with drifting stimuli of all orientations, and even obtained with stimuli that do not evoke V1 responses. A consequence of this type of suppression is contrast saturation.
2. Intracortical inhibition is principally responsible for surround suppression. This type of suppression is slow (tens of milliseconds), binocular, present well outside the receptive field, and strongest with stimuli with preferred orientation.
3. Intrinsic cellular mechanisms are principally responsible for visual adaptation. Adaptation is very slow (seconds), long lasting, binocular, and induced only by stimuli that drive the V1 neuron being adapted.
This schematic picture captures the results of a large body of literature, but it is surely not complete. Although it might take hundreds of milliseconds to reach its peak strength (F. Sengpiel, personal communication), dichoptic cross-orientation suppression has been observed (Sengpiel et al., 1998
Conclusions
The broad range of phenomena predicted by our model leads us to propose that synaptic depression, and not intracortical inhibition, is the primary mechanism by which V1 neurons adjust their responsiveness to spatially superimposed stimuli. Thus, we suggest a biophysical substrate that is alternative to our previous models, which were based on intracortical inhibition (Heeger, 1992a
Future work will be aimed at using our model to fit neuronal responses quantitatively. Indeed, although the responses of the model are the result of simulations, for grating and plaid stimuli, we have derived a closed-form mathematical equation that approximates the model responses (see Appendix). This equation is similar to the one that we derived previously for a model based on intracortical inhibition (Carandini et al., 1997
In conclusion, intracortical inhibition is still a candidate for a gain control mechanism (Carandini et al., 1999
FOOTNOTES Received July 9, 2002; revised Sept. 11, 2002; accepted Sept. 11, 2002.
This work was supported by the Human Frontiers Science Research Program Organization (M.C. and D.J.H.), the Silva Casa Foundation (W.S.), the National Eye Institute (R01-EY11794, D.J.H.), and the Swiss National Science Foundation (31-65234.01 to W.S. and 31-56007.98 to M.C.). We thank Sacha B. Nelson, Kenneth D. Miller, James R. Müller, and members of William T. Newsome's laboratory for helpful comments.
Correspondence should be addressed to Matteo Carandini, Smith-Kettlewell Eye Research Institute, 2318 Fillmore Street, San Francisco, CA 94115. E-mail: matteo{at}ski.org.
APPENDIX
In our model, physiological values such as currents, potentials, and firing rates are given units of spikes per second. This simplification reduces the number of model parameters. We held parameters fixed for all of our simulations, rather than individually tailoring them to yield the best match with published results.
LGN neurons
We define visual stimuli in terms of local contrast S(x, y, t) (i.e., with values between
1 and 1). The underlying linear response C(X, Y, T) of model LGN cells depends on the receptive field location X, Y, and on time T. This linear response is the convolution of a receptive field L with the stimulus S,
The output of ON-center cells and OFF-center cells is the rectified version of the positive and negative linear responses,
(2)
(3)
where
X
= X for (X 0) and 0 otherwise, and where we choose fmax = 100 spikes/sec and frest = 10 spikes/sec.
We model LGN receptive fields as the product of a function of time and a function of space.
where the function of space is a difference of Gaussians (Enroth-Cugell and Robson, 1966
with
c = 0.1°,
2, kr = 0.6deg
with
V1 neuron
The firing rate of our model V1 neuron is a rectified version of the membrane potential with threshold Vthresh = 5 spikes/sec (Carandini and Ferster, 2000
] with mean V and variance V
Contrast invariance of orientation selectivity is preserved in the transformation of membrane potential into firing rate, because this transformation behaves like a power function around spike threshold, and a power function retains contrast invariance (Heeger, 1992b
dv.](/content/vol22/issue22/fulltext/10053/img009.gif)
(4) Other than the spike threshold, the neuron is a passive membrane whose potential V is given by
where I is the synaptic current, and
(5) We chose a relatively long time constant,
The synaptic current is a weighted sum of the currents contributed by LGN neurons, with weights given by the receptive field strength,
where the sum is over a 12 × 12 grid of LGN cells covering 3° × 3°, centered on the origin. In our simple model of a synapse, synaptic activity results in current injection rather than in a conductance increase, as would be the case for a more realistic model. The postsynaptic current is thus simply I = p f, the product of the probability of synaptic transmission p and the presynaptic firing rate f. To distinguish synapses from ON-center and OFF-center cells, we write ION = pON fON and IOFF = pOFF fOFF. This expression is a simplification; in a more realistic model, synaptic excitation and inhibition would open conductances with appropriate reversal potentials. Here instead they result directly in the injection of positive and negative currents. This current injection behavior of synapses can, in fact, be accomplished thanks to the push-pull arrangement of excitation and inhibition (Carandini and Heeger, 1994
![I(t)=<LIM><OP>∑</OP><LL><UP>i, j</UP></LL></LIM>F(x<SUB><UP>i</UP></SUB>, y<SUB><UP>j</UP></SUB>)[I<SUB><UP>ON</UP></SUB>(x<SUB><UP>i</UP></SUB>, y<SUB><UP>j</UP></SUB>, t)−I<SUB><UP>OFF</UP></SUB>(x<SUB><UP>i</UP></SUB>, y<SUB><UP>j</UP></SUB>, t)],](/content/vol22/issue22/fulltext/10053/img011.gif)
(6) The spatial receptive field of our V1 neuron is given by a Gabor function (Hawken and Parker, 1987
where the proportionality factor is 10 over the volume under the Gaussian, and parameters are
=
/8, and
= 1 cycles/°. For many of the 144 LGN cells in the grid, synaptic weights assigned by the above expression are quite small. For example, for 60 LGN inputs, synaptic weights are <10% of maximum weight. As a result, although the number of LGN afferents to our model V1 neuron is high compared with current physiological estimates (Alonso et al., 2001
Synaptic depression
Thalamocortical synapses in the model are subject to synaptic depression. This effect occurs independently at each synapse. Synaptic depression follows presynaptic spikes instantaneously and recovers with a single time constant
After a presynaptic spike at time tspike, this resource is reduced by a factor u and then recovers to s = 1 with a single time constant
Time course of depression and recovery
To make the dynamics of depression evident, one can rewrite Equation 1 of Results as
where
The latter is equal to
Saturation in a depressing synapse
The saturation in Figure 1F is a well known property of synaptic depression (Abbott et al., 1997
Because the postsynaptic current is Ipost = p f and the presynaptic firing rate is f = k Ipre, where k is the gain of the presynaptic neuron (300 spikes per second per unit current), one can write
where Imax = 1/
Because the injected currents in Figure 1 vary slowly compared with the time constant of recovery
for different values of c. The approximate solution above would be exact if the stimulus frequency Predicted responses to plaids
The responses to plaids illustrated in Figure 4 can be approximated by a family of sigmoidal functions. This family of functions is more easily described for the membrane potential V than for the firing rate R, which is the output of a nonlinear mechanism. For the membrane potential V, the family of functions is given by
where V1 is the component of the membrane potential at the test frequency, ctest and cmask are test and mask contrasts, and Vmax and c50 are fixed parameters. To understand this expression intuitively, consider that without synaptic depression one would have only the term in the numerator; the response would grow linearly to the test contrast ctest regardless of the mask contrast cmask. The mask does not affect the responses, because the postsynaptic currents that it contributes sum to zero. Consider now synaptic depression in the absence of a mask (cmask = 0). We know from Figure 1 that responses will saturate with increasing contrasts; indeed, the expression above contains ctest both in the numerator and in the denominator. Finally, consider the effect of the mask. Because the mask depresses excitatory and inhibitory synapses equally, the postsynaptic currents that it contributes again sum to zero. Mask contrast cmask thus does not appear in the numerator. It appears in the denominator because the mask depresses the synapses as much as the test does. The above expression is simple and resembles that obtained in our previous model based on shunting inhibition (Carandini et al., 1997
REFERENCES
- Abbott LF, Varela JA, Sen K, Nelson SB (1997) Synaptic depression and cortical gain control. Science 275:220-224[Web of Science][Medline].
- Albrecht DG (1995) Visual cortex neurons in monkey and cat: effect of contrast on the spatial and temporal phase transfer functions. Vis Neurosci 12:1191-1210[Web of Science][Medline].
- Albrecht DG, Geisler WS (1991) Motion sensitivity and the contrast-response function of simple cells in the visual cortex. Vis Neurosci 7:531-546[Web of Science][Medline].
- Albrecht DG, Hamilton DB (1982) Striate cortex of monkey and cat: contrast response function. J Neurophysiol 48:217-237
[Free Full Text] .- Albrecht DG, Farrar SB, Hamilton DB (1984) Spatial contrast adaptation characteristics of neurones recorded in the cat's visual cortex. J Physiol (Lond) 347:713-739
[Abstract/Free Full Text] .- Albrecht DG, Geisler WS, Frazor RA, Crane AM (2002) Visual cortex neurons of monkeys and cats: temporal dynamics of the contrast response function. J Neurophysiol 88:888-913
[Abstract/Free Full Text] .- Allison JD, Smith KR, Bonds AB (2001) Temporal-frequency tuning of cross-orientation suppression in the cat striate cortex. Vis Neurosci 18:941-948[Web of Science][Medline].
- Alonso JM, Usrey WM, Reid RC (2001) Rules of connectivity between geniculate cells and simple cells in cat primary visual cortex. J Neurosci 21:4002-4015
[Abstract/Free Full Text] .- Anderson JS, Carandini M, Ferster D (2000a) Orientation tuning of input conductance, excitation and inhibition in cat primary visual cortex. J Neurophysiol 84:909-931
[Abstract/Free Full Text] .- Anderson JS, Lampl I, Gillespie DC, Ferster D (2000b) The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. Science 290:1968-1972
[Abstract/Free Full Text] .- Anderson JS, Lampl I, Gillespie DC, Ferster D (2001) Membrane potential and conductance changes underlying length tuning of cells in cat primary visual cortex. J Neurosci 21:2104-2112
[Abstract/Free Full Text] .- Bauman LA, Bonds AB (1991) Inhibitory refinement of spatial frequency selectivity in single cells of the cat striate cortex. Vision Res 31:933-944[Web of Science][Medline].
- Ben-Yishai R, Lev Bar Or R, Sompolinsky H (1995) Theory of orientation tuning in the visual cortex. Proc Natl Acad Sci USA 92:3844-3848
[Abstract/Free Full Text] .- Bishop PO, Coombs JS, Henry GH (1973) Receptive fields of simple cells in the cat striate cortex. J Physiol (Lond) 231:31-60
[Abstract/Free Full Text] .- Blakemore C, Tobin EA (1972) Lateral inhibition between orientation detectors in the cat's visual cortex. Exp Brain Res 15:439-440[Web of Science][Medline].
- Bolz J, Gilbert CD (1986) Generation of end-inhibition in the visual cortex via interlaminar connections. Nature 320:362-365[Medline].
- Bonds AB (1989) Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex. Vis Neurosci 2:41-55[Web of Science][Medline].
- Borg-Graham LJ, Monier C, Frégnac Y (1998) Visual input evokes transient and strong shunting inhibition in visual cortical neurons. Nature 393:369-373[Medline].
- Carandini M, Ferster D (1997) A tonic hyperpolarization underlying contrast adaptation in cat visual cortex. Science 276:949-952
[Abstract/Free Full Text] .- Carandini M, Ferster D (2000) Membrane potential and firing rate in cat primary visual cortex. J Neurosci 20:470-484
[Abstract/Free Full Text] .- Carandini M, Heeger DJ (1994) Summation and division by neurons in visual cortex. Science 264:1333-1336
[Abstract/Free Full Text] .- Carandini M, Ringach DL (1997) Predictions of a recurrent model of orientation selectivity. Vision Res 37:3061-3071[Web of Science][Medline].
- Carandini M, Mechler F, Leonard CS, Movshon JA (1996) Spike train encoding in regular-spiking cells of the visual cortex. J Neurophysiol 76:3425-3441
[Abstract/Free Full Text] .- Carandini M, Heeger DJ, Movshon JA (1997) Linearity and normalization in simple cells of the macaque primary visual cortex. J Neurosci 17:8621-8644
[Abstract/Free Full Text] .- Carandini M, Movshon JA, Ferster D (1998) Pattern adaptation and cross-orientation interactions in the primary visual cortex. Neuropharmacology 37:501-511[Web of Science][Medline].
- Carandini M, Heeger DJ, Movshon JA (1999) In: Linearity and gain control in V1 simple cells. Cerebral cortex, Vol 13, Models of cortical circuits (Peters A, ed), pp 401-443. New York: Kluwer Academic/Plenum.
- Carandini M, Heeger DJ, Senn W (2001) Cross-orientation suppression in V1 explained by synaptic depression. Soc Neurosci Abstr 27:12.12.
- Chagnac-Amitai Y, Connors BW (1989) Horizontal spread of synchronized activity in neocortex and its control by GABA-mediated inhibition. J Neurophysiol 61:747-758
[Abstract/Free Full Text] .- Chance FS, Abbott LF (2000) Input-specific adaptation in complex cells through synaptic depression. Neurocomputing 38-40:141-146.
- Chance FS, Nelson SB, Abbott LF (1998) Synaptic depression and the temporal response characteristics of V1 cells. J Neurosci 18:4785-4799
[Abstract/Free Full Text] .- Chung S, Li X, Nelson SB (2002) Short-term depression at thalamocortical synapses contributes to rapid adaptation of cortical sensory responses in vivo. Neuron 34:437-446[Web of Science][Medline].
- Crook JM, Kisvarday ZF, Eysel UT (1998) Evidence for a contribution of lateral inhibition to orientation tuning and direction selectivity in cat visual cortex: reversible inactivation of functionally characterized sites combined with neuroanatomical tracing techniques. Eur J Neurosci 10:2056-2075[Web of Science][Medline].
- Dean AF, Tolhurst DJ (1986) Factors influencing the temporal phase of response to bar and grating stimuli for simple cells in the cat striate cortex. Exp Brain Res 62:143-151[Web of Science][Medline].
- Dean AF, Tolhurst DJ, Walker NS (1982) Nonlinear temporal summation by simple cells in cat striate cortex demonstrated by failure of superposition. Exp Brain Res 45:456-458[Web of Science][Medline].
- DeAngelis GC, Robson JG, Ohzawa I, Freeman RD (1992) The organization of suppression in receptive fields of neurons in cat visual cortex. J Neurophysiol 68:144-163
[Abstract/Free Full Text] .- DeAngelis GC, Ohzawa I, Freeman RD (1993a) Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. I. General characteristics and postnatal development. J Neurophysiol 69:1091-1117
[Abstract/Free Full Text] .- DeAngelis GC, Ohzawa I, Freeman RD (1993b) Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. II. Linearity of temporal and spatial summation. J Neurophysiol 69:1118-1135
[Abstract/Free Full Text] .- DeAngelis GC, Freeman RD, Ohzawa I (1994) Length and width tuning of neurons in the cat's primary visual cortex. J Neurophysiol 71:347-374
[Abstract/Free Full Text] .- De Valois RL, De Valois K (1988) In: Spatial vision. Oxford: Oxford UP.
- Douglas RJ, Martin KAC (1998) Neocortex. In: The synaptic organization of the brain, Ed 4 (Shepherd GM, ed), pp 459-510. New York: Oxford UP.
- Douglas RJ, Martin KAC, Whitteridge D (1988) Selective responses of visual cortical cells do not depend on shunting inhibition. Nature 332:642-644[Medline].
- Douglas RJ, Koch C, Mahowald M, Martin KAC, Suarez HH (1995) Recurrent excitation in neocortical circuits. Science 269:981-985
[Abstract/Free Full Text] .- Enroth-Cugell C, Robson JG (1966) The contrast sensitivity of retinal ganglion cells of the cat. J Physiol (Lond) 187:517-552
[Abstract/Free Full Text] .- Eysel UT, Crook JM, Machemer HF (1990) GABA-induced remote inactivation reveals cross-orientation inhibition in the cat striate cortex. Exp Brain Res 80:626-630[Web of Science][Medline].
- Ferster D (1981) A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex. J Physiol (Lond) 311:623-655
[Abstract/Free Full Text] .- Ferster D (1988) Spatially opponent excitation and inhibition in simple cells of the cat visual cortex. J Neurosci 8:1172-1180[Abstract].
- Ferster D, Lindström S (1985) Augmenting responses evoked in area 17 of the cat by intracortical axons collaterals of cortico-geniculate cells. J Physiol (Lond) 367:217-232
[Abstract/Free Full Text] .- Fitzpatrick D (2000) Seeing beyond the receptive field in primary visual cortex. Curr Opin Neurobiol 10:438-443[Web of Science][Medline].
- Freeman TCB, Durand S, Kiper DC, Carandini M (2002) Suppression without inhibition in visual cortex. Neuron 35:759-771[Web of Science][Medline].
- Gardner JL, Anzai A, Ohzawa I, Freeman RD (1999) Linear and nonlinear contributions to orientation tuning of simple cells in the cat's striate cortex. Vis Neurosci 16:1115-1121[Web of Science][Medline].
- Glezer VD, Tscherbach TA, Gauselman VE, Bondarko VE (1982) Spatio-temporal organization of receptive fields of the cat striate cortex. Biol Cybern 43:35-49[Web of Science][Medline].
- Grieve KL, Sillito AM (1991) A re-appraisal of the role of layer VI of the visual cortex in the generation of cortical end inhibition. Exp Brain Res 87:521-529[Web of Science][Medline].
- Hammond P (1991) On the response of simple and complex cells to random dot patterns: a reply to Skottun, Grosof and De Valois. Vision Res 31:47-50[Web of Science][Medline].
- Hansel D, van Vreeswijk C (2002) How noise contributes to contrast invariance of orientation tuning in cat visual cortex. J Neurosci 22:5118-5128
[Abstract/Free Full Text] .- Hawken MJ, Parker AJ (1987) Spatial properties of neurons in the monkey striate cortex. Proc R Soc Lond B Biol Sci 231:251-288[Medline].
- Heeger DJ (1991) Nonlinear model of neural responses in cat visual cortex. In: Computational models of visual processing (Landy M, Movshon JA, eds), pp 119-133. Cambridge, MA: MIT.
- Heeger DJ (1992a) Normalization of cell responses in cat striate cortex. Vis Neurosci 9:181-197[Web of Science][Medline].
- Heeger DJ (1992b) Half-squaring in responses of cat simple cells. Vis Neurosci 9:427-443[Web of Science][Medline].
- Hirsch JA, Alonso JM, Reid RC, Martinez LM (1998) Synaptic integration in striate cortical simple cells. J Neurosci 18:9517-9528
[Abstract/Free Full Text] .- Holub RA, Morton-Gibson M (1981) Response of visual cortical neurons of the cat to moving sinusoidal gratings: response-contrast functions and spatiotemporal interactions. J Neurophysiol 46:1244-1259
[Free Full Text] .- Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat's visual cortex. J Physiol (Lond) 160:106-154
[Free Full Text] .- Hubel DH, Wiesel TN (1965) Receptive fields and functional architecture in two nonstriate visual areas (18-19) of the cat. J Neurophysiol 28:229-289
[Free Full Text] .- Jones JP, Palmer LA (1987) An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. J Neurophysiol 58:1233-1258
[Abstract/Free Full Text] .- Kayser A, Priebe NJ, Miller KD (2001) Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning. J Neurophysiol 85:2130-2149
[Abstract/Free Full Text] .- Koch C (1999) In: Biophysics of computation. New York: Oxford UP.
- Lampl I, Anderson JS, Gillespie DC, Ferster D (2001) Prediction of orientation selectivity from receptive field architecture in simple cells of cat visual cortex. Neuron 30:263-274[Web of Science][Medline].
- Lauritzen TZ, Krukowski AE, Miller KD (2001) Local correlation-based circuitry can account for responses to multi-grating stimuli in a model of cat V1. J Neurophysiol 86:1803-1815
[Abstract/Free Full Text] .- Li C-Y, Creutzfeldt O (1984) The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat. Pflügers Arch 401:304-314[Web of Science][Medline].
- Maffei L, Fiorentini A (1973) The visual cortex as a spatial frequency analyzer. Vision Res 13:1255-1267[Web of Science][Medline].
- Maffei L, Fiorentini A, Bisti S (1973) Neural correlate of perceptual adaptation to gratings. Science 182:1036-1038
[Abstract/Free Full Text] .- Maffei L, Berardi N, Bisti S (1986) Interocular transfer of adaptation after-effect in neurons of area 17 and 18 of split chiasm cats. J Neurophysiol 55:966-976
[Abstract/Free Full Text] .- Martin KAC (1988) From single cells to simple circuits in the cerebral cortex. Q J Exp Physiol 73:637-702
[Free Full Text] .- Martinez LM, Alonso JM, Reid RC, Hirsch JA (2002) Laminar processing of stimulus orientation in cat visual cortex. J Physiol (Lond) 540:321-333
[Abstract/Free Full Text] .- Miller KD, Troyer TW (2002) Neural noise can explain expansive, power-law nonlinearities in neural response functions. J Neurophysiol 87:653-659
[Abstract/Free Full Text] .- Morrone MC, Burr DC, Maffei L (1982) Functional implications of cross-orientation inhibition of cortical visual cells. I. Neurophysiological evidence. Proc R Soc Lond B Biol Sci 216:335-354[Medline].
- Morrone MC, Burr DC, Speed HD (1987) Cross-orientation inhibition in cat is GABA mediated. Exp Brain Res 67:635-644[Web of Science][Medline].
- Movshon JA, Lennie P (1979) Pattern-selective adaptation in visual cortical neurones. Nature 278:850-852[Medline].
- Movshon JA, Thompson ID, Tolhurst DJ (1978a) Spatial summation in the receptive fields of simple cells in the cat's striate cortex. J Physiol (Lond) 283:53-77
[Abstract/Free Full Text] .- Movshon JA, Thompson ID, Tolhurst DJ (1978b) Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat's visual cortex. J Physiol (Lond) 283:101-120
[Abstract/Free Full Text] .- Müller JR, Metha AB, Krauskopf J, Lennie P (1999) Rapid adaptation in visual cortex to the structure of images. Science 285:1405-1408
[Abstract/Free Full Text] .- Müller JR, Metha AB, Krauskopf J, Lennie P (2001) Information conveyed by onset transients in responses of striate cortical neurons. J Neurosci 21:6978-6990
[Abstract/Free Full Text] .- Murphy PC, Sillito AM (1987) Corticofugal feedback influences the generation of length tuning in the visual pathway. Nature 329:727-729[Medline].
- Murphy PC, Duckett SG, Sillito AM (1999) Feedback connections to the lateral geniculate nucleus and cortical response properties. Science 286:1552-1554
[Abstract/Free Full Text] .- Nelson S, Toth L, Sheth B, Sur M (1994) Orientation selectivity of cortical neurons during intracellular blockade of inhibition. Science 265:774-777
[Abstract/Free Full Text] .- Nelson SB (1991a) Temporal interactions in the cat visual system. I. Orientation-selective suppression in visual cortex. J Neurosci 11:344-356[Abstract].
- Nelson SB (1991b) Temporal interactions in the cat visual system. III. Pharmacological studies of cortical suppression suggest a presynaptic mechanism. J Neurosci 11:369-380[Abstract].
- Ohzawa I, Sclar G, Freeman RD (1985) Contrast gain control in the cat visual system. J Neurophysiol 54:651-665
[Abstract/Free Full Text] .- Palmer LA, Davis TL (1981) Receptive-field structure in cat striate cortex. J Neurophysiol 46:260-276
[Free Full Text] .- Reid RC, Alonso JM (1995) Specificity of monosynaptic connections from thalamus to visual cortex. Nature 378:281-284[Medline].
- Reid RC, Victor JD, Shapley RM (1992) Broadband temporal stimuli decrease the integration time of neuron in cat striate cortex. Vis Neurosci 9:39-45[Web of Science][Medline].
- Rushton WA, Henry GH (1968) Bleaching and regeneration of cone pigments in man. Vision Res 8:617-631[Web of Science][Medline].
- Sanchez-Vives MV, Nowak LG, McCormick DA (1998) Is synaptic depression prevalent in vivo and does it contribute to contrast adaptation? Soc Neurosci Abstr 24:896.
- Sanchez-Vives MV, Nowak LG, McCormick DA (2000a) Membrane mechanisms underlying contrast adaptation in cat area 17 in vivo. J Neurosci 20:4267-4285
[Abstract/Free Full Text] .- Sanchez-Vives MV, Nowak LG, McCormick DA (2000b) Cellular mechanisms of long-lasting adaptation in visual cortical neurons in vitro. J Neurosci 20:4286-4299
[Abstract/Free Full Text] .- Saul AB, Humphrey AL (1990) Spatial and temporal response properties of lagged and nonlagged cells in cat lateral geniculate nucleus. J Neurophysiol 64:206-224
[Abstract/Free Full Text] .- Saul AB, Humphrey AL (1992) Temporal-frequency tuning of direction selectivity in cat visual cortex. Vis Neurosci 8:365-372[Web of Science][Medline].
- Scanziani M (2000) GABA spillover activates postsynaptic GABA(B) receptors to control rhythmic hippocampal activity. Neuron 25:673-681[Web of Science][Medline].
- Sclar G, Freeman RD (1982) Orientation selectivity in the cat's striate cortex is invariant with stimulus contrast. Exp Brain Res 46:457-461[Web of Science][Medline].
- Sengpiel F, Baddeley RJ, Freeman TC, Harrad R, Blakemore C (1998) Different mechanisms underlie three inhibitory phenomena in cat area 17. Vision Res 38:2067-2080[Web of Science][Medline].
- Senn W, Buchs NJ (2002) Spike-based synaptic plasticity and the emergence of direction selective simple cells: mathematical analysis. J Comp Neurosci 13:167-186[Web of Science][Medline].
- Senn W, Markram H, Tsodyks M (2001) An algorithm for modifying neurotransmitter release probability based on pre- and postsynaptic spike timing. Neural Comput 13:35-67[Web of Science][Medline].
- Sillito AM (1975) The contribution of inhibitory mechanisms to the receptive field properties of neurones in the cat's striate cortex. J Physiol (Lond) 250:304-330.
- Skottun BC, Grosof DH, Valois RLD (1991) On the responses of simple and complex cells to random dot patterns. Vision Res 31:43-46[Web of Science][Medline].
- Smith MA, Bair W, Cavanaugh JR, Movshon JA (2001) Latency of inhibition from inside and outside the classical receptive field in macaque V1 neurons. Paper presented at the 2001 Vision Sciences Society Meeting, Sarasota, FL. J Vis 1:35a.
- Somers DC, Nelson SB, Sur M (1995) An emergent model of orientation selectivity in cat visual cortical simple cells. J Neurosci 15:5448-5465[Abstract].
- Stratford KJ, Tarczy-Hornoch K, Martin KAC, Bannister NJ, Jack JJ (1996) Excitatory synaptic inputs to spiny stellate cells in cat visual cortex. Nature 382:258-261[Medline].
- Thomson AM, Deuchars J (1997) Synaptic interactions in neocortical local circuits: dual intracellular recordings in vitro. Cereb Cortex 7:510-522
[Abstract/Free Full Text] .- Tolhurst DJ, Dean AF (1987) Spatial summation by simple cells in the striate cortex of the cat. Exp Brain Res 66:607-620[Web of Science][Medline].
- Tolhurst DJ, Dean AF (1990) The effects of contrast on the linearity of spatial summation of simple cell in the cat's striate cortex. Exp Brain Res 79:582-588[Web of Science][Medline].
- Tolhurst DJ, Walker NS, Thompson ID, Dean AF (1980) Nonlinearities of temporal summation in neurones in area 17 of the cat. Exp Brain Res 38:431-435[Web of Science][Medline].
- Troyer TW, Krukowski AE, Priebe NJ, Miller KD (1998) Contrast-invariant orientation tuning in cat visual cortex: thalamocortical input tuning and correlation-based intracortical connectivity. J Neurosci 18:5908-5927
[Abstract/Free Full Text] .- Tsodyks MV, Markram H (1997) The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94:719-723
[Abstract/Free Full Text] .- Varela JA, Sen K, Gibson J, Fost J, Abbott LF, Nelson SB (1997) A quantitative description of short-term plasticity at excitatory synapses in layer 2/3 of rat primary visual cortex. J Neurosci 17:7926-7940
[Abstract/Free Full Text] .- Volgushev M, Vidyasagar TR, Pei X (1996) A linear model fails to predict orientation selectivity of cells in the cat visual cortex. J Physiol 496(3):597-606
[Abstract/Free Full Text] .- Walker GA, Ohzawa I, Freeman RD (1998) Binocular cross-orientation suppression in the cat's striate cortex. J Neurophysiol 79:227-239
[Abstract/Free Full Text] .
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